The concepts of atmospheric refraction and atmospheric dispersion are introduced and the method of how to eliminate atmospheric dispersion. This article introduces the structure of Atmospheric Dispersion Correction , the installation position of ADC in TMT telescope and the introduction to the principle of ADC in detail. Using the finite element analysis software Ansys Workbench to analyze the rationality of the ADC structure. Static analysis The ADC structure is loaded with two tape lens, which is more 400kg in weight, as well as itself weight, will deform in x, y, z directions. Dynamic analysis The dynamic performances of ADC structure are very important for the construction of the instrument, for the environmental vibration need to be tested. That is the effect of ADC dynamic deformation on optical accuracy is crucial for imaging quality. Here three order modes of dynamic performance are presented for the references of ADC design. They are 1st order mode , 2nd order mode and 3rd order mode. Thermal deformation according to the ADC working environment temperature change, the instrument temperature would be from -5 to 9 degree. So the thermal deformation of ADC is performed in this temperature fluctuation. ADC structure FEA conclusions: The ADC tapered lens are assumed as a rigid body and the mechanical analysis results are: Static analysis, Kinetics analysis and Thermodynamic analysis. Based on the FEA results, we get the image motion information in the telescope plane. Then, we draw a conclusion that: image motions induced by current structure design are very small and meet the requirements of ADC.